A source told us, “Bianca is a very accomplished woman and has started to accompany Booker to certain events. But both have very demanding jobs — he in DC, and Bianca in Los Angeles.”

Levin was even listed in the Hollywood Reporter’s “Hollywood’s Fastest-Rising Stars” in 2011, at which time she told the publication she’s focusing on signing emerging talent. “People take on entertainment lawyers very early in their careers now, so it’s super-competitive,” she says. “You’ve got to always be on the lookout for great talent.”

In an August interview with the Washington Post, Booker, 44, talked about his “great dismay” that he has not “settled down with a life partner.”

Booker said, “People who think I’m gay, some part of me thinks it’s wonderful. Because I want to challenge people on their homophobia. I love seeing on Twitter when someone says I’m gay, and I say, ‘So what does it ­matter if I am?’ ”

A spokesman for Booker said, “We don’t comment on the senator’s personal life.” Calls to Levin’s office were not returned.